A specialized racing yacht has a structural keel of length 1.8 m. The keel has a symmetrical cross-section as shown in the design specifications, where d d\,d represents the horizontal distance from the center plane and v v\,v represents the vertical depth below the hull waterline, both measured in centimetres. The table below provides the depth profile for one half of the symmetrical cross-section.
d048121620v−18.0−17.65−16.32−13.48−8.550 \begin{array}{|c|c|c|c|c|c|c|}\hline d & 0 & 4 & 8 & 12 & 16 & 20 \\ \hline v & -18.0 & -17.65 & -16.32 & -13.48 & -8.55 & 0 \\ \hline \end{array} dv0−18.04−17.658−16.3212−13.4816−8.55200Use the trapezium rule with all the values in the table to find the best estimate for the total displacement volume of the keel in cm3\text{cm}^3cm3.
Practise Edexcel A Level Maths 11.9 The Trapezium Rule with exam-style questions for A Level Maths. 44 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
